Properties

Label 2.193.abw_bkq
Base Field $\F_{193}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{193}$
Dimension:  $2$
L-polynomial:  $1 - 48 x + 952 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0675123601384$, $\pm0.230069799779$
Angle rank:  $2$ (numerical)
Number field:  4.0.2054400.4
Galois group:  $D_{4}$
Jacobians:  60

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 60 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28890 1372679460 51673224895290 1925154747813891600 71709016301977158272250 2671085051932861814910021540 99495244227359262020013683985690 3706098379840788899452903641725337600 138048458691010890857009571047801225160090 5142167038122541242600917679806266810857166500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 146 36850 7187762 1387510918 267785600306 51682541600050 9974730240873362 1925122950833556478 371548729888542460946 71708904873245099619250

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.2054400.4.
All geometric endomorphisms are defined over $\F_{193}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.bw_bkq$2$(not in LMFDB)